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Bertrand Mareschal

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Abstract
« on: April 08, 2020, 02:58:56 PM »
Promethee methods: sensibility study & remarks
In the case of a decision rule based on an aggregation function that places us in the Arrow’s theorem
context, it is not possible to check some mathematical properties simultaneously. Indeed, to
construct a method using the same concepts, we can not abandon the principles of unanimity,
universality and non-dictatorship. Thus, the only two principles between which we have to choose
are the transitivity and the independence. In other words, it is impossible to build an ordinal method
verifying the transitivity and the independence at the same time. A thorough analysis has shown the
impossibility to find and\or define MCDM methods satisfying some derived mathematics properties
simultaneously.
In this paper, we study the sensibility of Promethee family methods to the use of different versions
of independence and transitivity. On this basis, we construct rules and mathematical conditions
upon which Promethee family keep their original results. In case of change of the original
outranking, we propose post-optimality studies and enquiries allowing to expect the new results and
their values.
MCDM methods; performance evaluation; preference modelling; multicriteria analysis; Promethee;
independence property; transitivity property.
References
[1] Brans, J. P.& Mareschal, B. (1997) How to decide with PROMETHEE, ULB and VUB Brussels Free
Universities, Research repport.
[2] Brans, J. P.& Mareschal, B. (2001) PROMETHEE-Gaia : une méthodologie d’aide à la décision en présence
de critères multiples, éditions de l’université de Bruxelles, Ellipses.
[3] Doignon, J.-P., Monjardet, B., Roubens, M. & Ph. Vincke, (1986) Biorder families,valued relations, and
preference modelling, Elsevier Science : Journal of Mathematical Psychology, vol.30(4), p.435–480.
[4] Pirlot, M. and Vincke, P. (1997) Semiorders : Properties, Representations, Applications, Springer Netherlands
: Theory and Decision Library B.
[5] Vincke, Ph., (1982) Arrow’s theorem is not a surprising result, Elsevier Science : Europeanjournal of
operational research, vol.10(1), p.22–25.
[6] Vincke, Ph. (1992) Exploitation of a crisp relation in a ranking problem, Springer US : Theory and Decision,
vol.32(3), p.221–240.
Bertrand